Question: Simplify. Rewrite the expression in the form $y^n$. $\left(y^2\right)^{3}=$
Solution: $\begin{aligned} \left(y^2\right)^{3}&=y^{2\cdot 3} \\\\ &=y^{6} \end{aligned}$ This follows from the general rule $\left(x^m\right)^{n}=x^{m\cdot n}$. We can also see this is correct by expanding the powers. $\begin{aligned} \left(y^2\right)^{3}&=\underbrace{y^2\cdot y^2\cdot y^2}_\text{3 times} \\\\\\ &=\underbrace{ \underbrace{y\cdot y}_\text{2 times} \cdot \underbrace{y\cdot y}_\text{2 times} \cdot \underbrace{y\cdot y}_\text{2 times}} _\text{3 times} \\\\ &=y^{6} \end{aligned}$ In conclusion, $\left(y^2\right)^{3}=y^{6}$.